Amplitudes within causal loop-tree duality

TL;DR

This paper develops a method for calculating scalar one-loop amplitudes in massive -theory using causal loop-tree duality, deriving recurrence relations and verifying results up to seven points with Monte Carlo integration.

Contribution

It introduces a recurrence relation for the integrand of one-loop amplitudes that is free of spurious singularities, improving computational efficiency and accuracy.

Findings

Results agree with analytic calculations up to seven points.

The integrand is free of spurious singularities on H-surfaces.

Monte Carlo integration successfully computes the amplitudes.

Abstract

We study scalar one-loop amplitudes in massive $\phi^3$-theory within causal loop-tree duality. We derive a recurrence relation for the integrand of the amplitude. The integrand is by construction free of spurious singularities on H-surfaces. Taking renormalisation and contour deformation into account, we obtain the (integrated) amplitude by Monte Carlo integration. We have checked up to seven points that our results agree with analytic results.